Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 03, pp. 1-8.

Title: An approximation property of Gaussian functions
        
Authors: Soon-Mo Jung  (Hongik Univ., Jochiwon, South Korea)
         Hamdullah Sevli (Istanbul Commerce Univ., Turkey)
         Sebaheddin Sevgin (Yuzuncu Yil Univ., Van, Turkey)

Abstract:
 Using the power series method, we solve the inhomogeneous
 linear first order differential equation
 $$
 y'(x) + \lambda (x-\mu) y(x) = \sum_{m=0}^\infty a_m (x-\mu)^m,
 $$
 and prove an approximation property of Gaussian functions.

Submitted  October 5, 2012. Published January 07, 2013.
Math Subject Classifications: 34A30, 34A40, 41A30, 39B82, 34A25.
Key Words: Linear first order differential equation;
           power series method; Gaussian function; approximation;
           Hyers-Ulam stability; local Hyers-Ulam stability.